The earth""s gravitation field varies between a low of about 880 mgals at the equator to about 1,100 mgals at the poles with gradients characterized in Eotvos units, where one Eotvos unit equals 10xe2x88x929secxe2x88x922. For an idealized homogeneous sphere, an equipotential surface outside of the sphere is also spherical, and, for any relatively small volume unit in free space, an idealized gravity field can be viewed as a set of unidirectional field lines aligned along the local vertical and having zero magnitude in the x,y directions. In the context of a geoshpere such as the earth, density inhomogeneities in the geosphere give rise to an equipotential surface that is not spherical, i.e., the curvature of any point is different in different directions. In the context of the earth, local variations in gravity are caused by deviations in the surface of the earth from a geometric sphere, surface geology, water tides, atmospheric tides, and the change in relative position of the earth, the moon, and the sun.
For any observation point within an arbitrary volume unit, the gravity field at that observation point can be resolved into x,y,z components of which the z vector will have the largest magnitude and the x,y vectors will have respective magnitudes that are a function of the location of that observation point relative to any mass inhomogenieties.
FIG. 1 illustrates a conventional coordinate system in which the X axis corresponds to the north-south alignment, the Y axis corresponds to the east-west alignment, and the Z axis corresponds to the up-down alignment. Using this coordinate system convention and for any observation point, the gravity gradient is a second order derivative of the gravity potential scaler xcex93 and is represented by a second-order nine-component symmetric tensor xcex93ij as shown in FIG. 2.
The components xcex93x,x and xcex93y,y are approximately equal to the variation of the force of gravity along the x and y directions, respectively, and are known as the horizontal gradient components, and xcex93z,z is known as the vertical gradient of gravity. Three pairs of the nine elements are symmetrically equal, i.e., xcex93x,z=xcex93z,x, xcex93y,z=xcex93z,y, and, lastly, xcex93x,y=xcex93y,x so that the tensor is characterized by five independent components. Additionally, the diagonal elements are scalar invariant and conform to the Laplacian relationship:
0=xcex93x,x+xcex93y,y+xcex93z,zxe2x80x83xe2x80x83EQ. 1
from which it follows that:
xcex93z,z=xe2x88x92(xcex93x,x+xcex93y,y)xe2x80x83xe2x80x83EQ. 2
Two general types of instruments, characterized in a generic sense as xe2x80x9cabsolutexe2x80x9d and xe2x80x9crelativexe2x80x9d instruments, have been developed for measuring, directly or indirectly, the various components within the gravity tensor.
In general, the gravity field along the z axis can be measured by uniaxis gravimeters of which a common type uses lasers and a high-precision clock to time a mass falling between two vertically spaced points in an evacuated space. Gradiometers, as distinguished from gravimeters, measure the curvature gradients (or differential curvature or ellipticity of the gravity equipotential surfaces), horizontal gradients (or the rate of change of the increase of gravity in the horizontal direction), or vertical gradients (or the rate of increase of gravity in the vertical direction).
An absolute gravity instrument that relies on the direct measurement of a mass whose movement is a function the of gravity field is disclosed in U.S. Pat. No. 5,351,122 issued Sep. 27, 1994 to T. Niebauer et al. As disclosed therein, the instrument utilizes a reflective mass that is dropped under the influence of gravity. The motion of the free-falling reflective mass is measured using a split-beam laser interferometer by which light from a laser is split into two paths with light from one of the paths reflected from the free-falling reflective mass and the reflected light compared with light from the other path. Since the instrument is relatively simple and the falling mass is influenced directly by the gravity field, the value of gravity can be accurately calculated using Newtonian principles.
A more sophisticated absolute gravity measuring instrument is disclosed in U.S. Pat. No. 5,892,151 issued Apr. 6, 1999 to T. Niebauer et al. which discloses the use of two physically spaced-apart falling body sensors to obtain a differential measurement of gravity. Where two of the sensors are spaced apart from one another along the vertical axis, differences in the measured output of sensors represents the component xcex93z,z of the gravity tensor. The differential instrument is well-suited for use in those applications in which differential gravity measurement are desired, including mineral and petroleum exploration and extraction.
In contrast to the falling-body absolute gravity instruments, one type of relative instrument utilizes plural pairs of accelerometers that are moved at a constant velocity along an orbital path about a spin axis. Information from each accelerometer at any angular position in the orbit provides information as to the lateral acceleration, including the gravity field, sensed by the accelerometers. A representative relative instrument is disclosed in U.S. Pat. No. 5,357,802 issued Oct. 25, 1994 to Hofmeyer and Affleck and entitled xe2x80x9cRotating Accelerometer Gradiometerxe2x80x9d and sold in various forms by the Lockheed Martin corporation (Buffalo N.Y. USA). The Lockheed Martin instrument is designed to measure the local gravity gradient and includes plural pairs of accelerometers mounted at a common radius and equi-spaced about the periphery of a rotor assembly that is rotated at a constant and controlled angular velocity about a spin axis.
Each accelerometer provides a sinusoidally varying analog output that is a function of the acceleration experienced by each accelerometer as the accelerometer orbits the spin axis. For a gradiometer having its spin axis aligned along the field lines in an ideally uniform and unperturbed gravity field, each accelerometer experiences the same acceleration forces as its proceeds along its orbital path. However, where the local gravity field is perturbed by the presence of one or more masses and/or the spin axis is tilted relative to the local vertical field lines, each accelerometer will experience different accelerations throughout its orbit. The quantitative output of each accelerometer, coupled with its rotary position, provides information related to the local gravity gradients.
Gradiometers of the type that employ orbiting accelerometers must use accelerometers with precisely matched physical properties, matched scale factors, various servo loops that are linear and stable, and numerous other control and feedback loops that must remain uniformly stable with time. Various signal processing techniques, principally common mode rejection techniques, have been used to reduce and minimize errors sources to improve measurement accuracy. Errors sources include mis-matched scale factors, motor and bearing vibration, stray electromagnetic fields, and the usual array of electronic noise sources. Because of the complexity of accelerometer-type gradiometers, the accuracy and repeatability of the devices are strongly influenced by temperature, pressures, and duration of service requiring periodic instrument calibrations and monitoring of time-dependent drift errors. Additionally, the overall instrument transfer function is frequency dependent and includes specific frequencies for which the instrument is maximally sensitive. At these frequencies, it can be difficult to separate information in the output power spectrum that represents the desired gravity information and non-information noise. Since the accelerometers in these types of gradiometers do not directly measure gravity in the same direct manner as a falling-body instrument, the output can only be characterized in the context of a relative difference.
In view of the above, it is an object of the present invention, among others, to provide a complemented absolute/relative full-tensor gravity gradiometer system having enhance functionality and measurement veracity.
It is another object of the present invention to provide a complemented absolute/relative full-tensor gravity gradiometer system using a gradiometer and a gravimeter to provide enhanced accuracy outputs.
The present invention provides a complemented absolute/relative full-tensor gravity gradiometer system by which two different types of instruments, neither of which measures the full gravity tensor and which have different error sources, provide their respective partial gravity tensor outputs to construct a composite full gravity tensor in which selected gravity components within the composite tensor are compared for the purpose of monitoring that instrument having the larger number of error sources to enhance the reliability of the output of that instrument.
In the preferred form of the invention, an absolute gravity instrument, which depends upon direct measurement of a moving mass, provides partial gravity tensor outputs that have a high degree of repeatability, low error sources, and provide outputs that are quantifiable by Newtonian rules. A relative gravity instrument, such as a gradiometer, also provides its particular partial gravity tensor outputs. Based upon known mathematical relationships within the tensor, including equalities between off-diagonal components of the tensor and the zero-sum relationship of the in-line diagonal components, the outputs of one instrument can verify the reasonability of the output of the other instruments and be used to identify out-of-calibration operation of the other instrument.
In the preferred embodiment of the present invention, an absolute gravity instrument of the type that utilizes a reflective body that free-falls in a drop zone is complemented with a relative gravity instrument that utilizes orbiting accelerometer pairs to provide relative gravity information. The absolute gravity instrument can include at least two sensors that are vertically spaced, one above the other, to provide the xcex93z,z component of the gravity gradient and other sensors that are laterally spaced therefrom to provide the xcex93z,k and xcex93z,y components. Since the free-falling reflective mass of each sensor is directly influenced by gravity and the measurement is optical, the gravity values are quantifiable using Newtonian principles and information outputs of the absolute gravity instrument can be considered to be an absolute gravity measurement with minimal noise and errors sources. Concurrently, the relative gravity instrument provides its output contributions to the gravity tensors, i.e., the xcex93x,x xcex93x,y xcex93x,z xcex93y,x xcex93y,y and xcex93y,z components.
The known equalities of various off-diagonal components of the gravity tensor (e.g., xcex93x,z=xcex93z,x=xcex93y,z xcex93z,y, and xcex93x,y=xcex93y,x) and the zero-sum relationship of the diagonal components (xcex93x,x+xcex93y,y+xcex93z,z=0) are used with respective device outputs to increase the reliability, repeatability, and reasonableness of the output of the relative gravity instrument. Thus, the xcex93y,z output of the absolute instrument is compared to the xcex93z,y output of the relative instrument and any inequalities therebetween used to evaluate, correct, or compensate the output of the relative instrument. In a similar manner, the xcex93z,x output of the absolute instrument is correlated or compared against the xcex93x,z output of the relative instrument and any inequalities therebetween use to evaluate, correct, or compensate the output of the relative instrument. Additionally, the xcex93z,z output of the absolute instrument is checked against the sum of the xcex93x,x and xcex93yy outputs as a way of checking the reasonableness of the outputs of the relative instrument.
The present invention advantageously provides a complemented absolute/relative full-tensor gravity gradiometer system in which the gradiometer and the gravimeter components of the system provide accuracy-enhanced outputs.
Other objects and further scope of applicability of the present invention will become apparent from the detailed description to follow, taken in conjunction with the accompanying drawings, in which like parts are designated by like reference characters.